Gauss hypergeometric function 2F1: Specific values (formula 07.23.03.c6ma)

Hypergeometric2F1

$Mathematica Notation$

Hypergeometric Functions

Hypergeometric2F1[a,b,c,z]

Specific values

For rational parameters with denominators 8 and fixed z and a>0

For fixed z and a=17/8, b>=a

For fixed z and a=17/8, b=39/8

http://functions.wolfram.com/07.23.03.c6ma.01

Input Form

Hypergeometric2F1[17/8, 39/8, -(7/2), -z] == (1/(1277696 (1 + z)^(21/2))) (Sqrt[1 + z] (1277696 + 16598640 z + 109704319 z^2 + 553124723 z^3 + 4004220834 z^4 - 7728762714 z^5 + 894061155 z^6 + 63649287 z^7 + 3515148 z^8) Cosh[ArcSinh[Sqrt[z]]/4] - Sqrt[z] (319424 + 4249480 z + 28680425 z^2 + 146325425 z^3 + 25721480982 z^4 - 21969216246 z^5 + 925446405 z^6 + 65406861 z^7 + 3515148 z^8) Sinh[ArcSinh[Sqrt[z]]/4])

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]